The grades on a history midterm at Loyola are normally distributed with $\mu = 73$ and $\sigma = 2.0$. Nadia earned a $71$ on the exam. Find the z-score for Nadia's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Nadia's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{71 - {73}}{{2.0}}} $ ${ z \approx -1.00}$ The z-score is $-1.00$. In other words, Nadia's score was $1.00$ standard deviation below the mean.